U.S. patent application number 14/595025 was filed with the patent office on 2015-07-16 for mobile terminal antenna alignment using arbitrary orientation attitude.
The applicant listed for this patent is ViaSat, Inc.. Invention is credited to Clifford K. Burdick, Arthur S. Loh, David H. Schmitz, Brian T. Sleight.
Application Number | 20150200449 14/595025 |
Document ID | / |
Family ID | 53522113 |
Filed Date | 2015-07-16 |
United States Patent
Application |
20150200449 |
Kind Code |
A1 |
Sleight; Brian T. ; et
al. |
July 16, 2015 |
Mobile Terminal Antenna Alignment Using Arbitrary Orientation
Attitude
Abstract
Systems and methods for aligning a satellite antenna mounted on
a mobile platform to the platform. At each of several arbitrary
orientations, a first directional vector is determined from the
antenna to a satellite. For each orientation, an alias
transformation is performed to transform the first vector having
coordinates defined with respect to a first reference frame to a
second vector having coordinates defined with respect to a second
reference frame. A third vector is determined based on the
orientation of the antenna after peaking the antenna. A rotation
matrix is derived from the collection of second and third vectors.
An estimate of the rotational offset of the satellite antenna with
respect to the platform is determined based on the rotation matrix.
The rotational offset is applied to the attitude of the platform to
accurately point the antenna to the satellite.
Inventors: |
Sleight; Brian T.;
(Carlsbad, CA) ; Schmitz; David H.; (Encinitas,
CA) ; Burdick; Clifford K.; (Vista, CA) ; Loh;
Arthur S.; (San Diego, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
ViaSat, Inc. |
Carlsbad |
CA |
US |
|
|
Family ID: |
53522113 |
Appl. No.: |
14/595025 |
Filed: |
January 12, 2015 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61927322 |
Jan 14, 2014 |
|
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Current U.S.
Class: |
342/352 |
Current CPC
Class: |
H01Q 3/08 20130101; H01Q
1/28 20130101 |
International
Class: |
H01Q 3/02 20060101
H01Q003/02 |
Claims
1. An antenna alignment module (AAM) comprising: a. a first output
port through which the AAM provides control signals to control the
position of a satellite antenna; b. at least one processor
configured to: i. take a first attitude measurement in a first
orientation, including: 1. receiving information indicating the
location of a platform and the location of a satellite; 2.
determining a first vector {right arrow over (d)}.sub.i from the
satellite antenna to the satellite based on the location of the
platform and the location of the satellite, the first vector {right
arrow over (d)}.sub.i being represented by coordinates defined with
respect to a first reference frame; 3. receiving information
indicating the attitude of a position and attitude measurement
device (PAMD) when the platform is in the first orientation the
attitude of the PAMD, the platform and the antenna remaining
essentially unchanged with respect to each other as the orientation
of the platform changes; and 4. determining a second vector {right
arrow over (d)}'.sub.i by performing an alias transformation on the
first vector {right arrow over (d)}.sub.i, the alias transformation
transforming the coordinates of the first vector {right arrow over
(d)}.sub.i from the first reference frame to a second reference
frame based on the attitude of the PAMD when in the first
orientation; 5. receiving information indicating the attitude of
the satellite antenna when peaked to the satellite with the
platform in the first orientation; 6. determining a third vector
{right arrow over (d)}''.sub.i from the satellite antenna to the
satellite based on the received information indicating the attitude
of the satellite antenna when peaked to the satellite, the third
vector {right arrow over (d)}''.sub.i being represented in
coordinates defined with respect to a third reference frame ii.
take additional attitude measurements in additional orientations to
accumulate a collection of second vectors {right arrow over
(d)}'.sub.i and third vectors {right arrow over (d)}''.sub.i; iii.
determine a first rotation matrix {circumflex over (T)} based on
the collection of second vectors {right arrow over (d)}'.sub.i and
third vectors {right arrow over (d)}''.sub.i; iv. determine a roll,
pitch and yaw offset between the attitude of the PAMD and the
attitude of the satellite antenna based on the rotation matrix; and
v. outputting control signals for pointing the satellite antenna at
the satellite based on the roll, pitch and yaw offsets.
2. The AAM of claim 1, wherein the control signals output for
pointing the satellite antenna include information regarding the
azimuth and elevation to which to move the antenna to point the
antenna at the satellite.
3. The AAM of claim 1, wherein the control signals output for
pointing the satellite antenna include the roll, pitch and yaw
offsets.
4. The AAM of claim 1, further including at least one input port
through which the AAM receives information regarding at least one
of the following: a. the attitude of a PAMD mounted on the platform
on which the satellite antenna is mounted; b. the location of the
platform; c. a location of a satellite; and d. the attitude of the
satellite antenna.
5. The AAM of claim 1, further including the PAMD.
6. The AAM of claim 1, wherein the location of the satellite and
the location of the platform are each represented by coordinates
defined with respect to the first reference frame.
7. The AAM of claim 1, wherein receiving the information indicating
the attitude of the PAMD when the platform is in the first
orientation includes: a. determining the attitude of the PAMD at a
first time prior to the platform being in the first orientation; b.
determining a rate of change in the attitude of the PAMD at the
first time; and c. determining the attitude of the PAMD at a second
time when the platform is in the first orientation from the
attitude and rate of change in the PAMD determined at the first
time.
8. The AAM of claim 1, wherein receiving the information indicating
the attitude of the platform when the platform is in the first
orientation includes: a. determining the attitude of the PAMD at a
first time, the first time occurring after the platform was in the
first orientation; b. determining a rate of change of the attitude
of the PAMD at the first time; and c. determining the attitude of
the PAMD when the platform was in the first orientation from the
attitude and the rate of change determined at the first time.
9. The AAM of claim 1, wherein the platform is an aircraft.
10. The AAM of claim 9, wherein the aircraft is on the ground in
the first orientation.
11. The AAM of claim 10, wherein the aircraft is rotated on the
ground to each of the additional orientations.
12. The AAM of claim 9, wherein at least some of the attitude
measurements are taken in flight.
13. The AAM of claim 9, wherein at least some of the attitude
measurements are taken during ground movement of the aircraft.
14. The AAM of claim 1, wherein the information indicating the
attitude of the satellite antenna is received from an antenna
positioning motor.
15. The AAM of claim 1, wherein the information indicating the
attitude of the satellite antenna is received from position
determining sensors coupled to the antenna.
16. The AAM of claim 4, wherein the information regarding attitude
of the platform is received from a Position and Attitude
Measurement Device (PAMD).
17. The AAM of claim 16, wherein the PAMD includes at least an
Inertial Reference Unit (IRU).
18. The AAM of claim 17, the PAMD further including a global
positioning system (GPS), the GPS providing the location of the
platform to the AAM.
19. The AAM of claim 1, wherein pointing the satellite antenna at
the satellite includes: a. receiving the attitude of the platform;
b. determining a fourth vector from the platform to the satellite
based on the location of the satellite and the location of the
platform; c. performing an alias transformation on the fourth
vector based on the attitude of the platform to determine a fifth
vector; d. performing a second alias transformation on the fifth
vector based on the roll, pitch, and yaw offsets to determine a
sixth vector; and e. pointing the antenna at the satellite based on
the sixth vector.
20. The AAM of claim 19, wherein pointing the antenna at the
satellite includes determining the azimuth and elevation to be
provided to an antenna positioning motor from the sixth vector.
21. The AAM of claim 1, the processor further configured to account
for an error in the information indicating the attitude of the
satellite antenna when peaked to the satellite.
22. The AAM of claim 21, the error in the information indicating
the attitude of the satellite antenna including an error in the
elevation of the satellite antenna when peaked to the
satellite.
23. The AAM of claim 21, the processor further configured to
perform the alias transformation on the first vector by multiplying
the first vector by a second rotation matrix M.sub.i and the
processor further configured to account for the error in the
information indicating the attitude of the satellite antenna when
peaked to the satellite by multiplying the third vector by the
transpose of an orthogonalized version of the first rotation matrix
{circumflex over (T)} and by the transpose of the second rotation
matrix M.sub.i.
24. A method for aligning an antenna to an attitude determining
device having an attitude that remains essentially unchanged with
respect to the antenna when an orientation of a platform on which
the antenna and the attitude determining device are mounted
changes, the antenna having an antenna reference frame and the
attitude determining device having an attitude determining device
reference frame, the method comprising: a. taking a first attitude
measurement at a first platform orientation to determine: i. a
first vector {right arrow over (d)} from the antenna to a
satellite, the first vector being determined based on the location
of the platform as determined by a position measuring device and a
location of the satellite; and ii. a second vector {right arrow
over (d)}'.sub.i by performing an alias transformation on the first
vector {right arrow over (d)} from a first reference frame to a
second reference frame based on the attitude of the platform; iii.
a third vector {right arrow over (d)}''.sub.i from the antenna to a
satellite when the antenna is peaked to the satellite, the third
vector being represented by coordinates defined with respect to a
third reference frame, the third vector {right arrow over
(d)}''.sub.i being determined based on information indicating the
attitude of the antenna; b. taking additional measurements at a
plurality of other platform orientations, each measurement
determining a first vector, second vector and third vector for the
associated platform orientation, resulting in a collection of
second and third vectors; c. determining a first rotation matrix
based on the collection of second and third vectors; d. determining
a rotational offset between the antenna and the platform based on
the first rotation matrix; and e. pointing the satellite antenna at
the satellite based on the rotational offset.
25. The method of claim 24, wherein the rotational offset is an
offset in roll, pitch and yaw with respect to the second reference
frame.
26. The method of claim 24, further including: a. using the roll,
pitch and yaw offset to determine a second rotation matrix; b.
receiving information indicating the location of the satellite; c.
receiving information indicating the location of the platform; d.
determining a fourth vector based on the location of the satellite
and the location of the platform; e. receiving attitude information
indicating the attitude of the platform; f. determining a fifth
vector by performing an alias transformation on the fourth vector
from the first reference frame to the second reference frame based
on the attitude of the platform; and g. determining a sixth vector
by performing an alias transformation on the fifth vector using the
second rotation matrix; and h. pointing the antenna to the
satellite based on the sixth vector.
27. The method of claim 24, wherein the platform is an
aircraft.
28. The method of claim 24, wherein the attitude of the platform is
determined based on the output from a position and attitude
determining device (PAMD).
29. The method of claim 28, wherein the PAMD is an inertial
reference unit (IRU).
30. The method of claim 29, wherein the PAMD includes a global
positioning system to determine the location of the platform.
31. The method of claim 24, wherein the information indicating the
attitude of the antenna is provided by an antenna positioning
motor.
32. The method of claim 24, wherein the information indicating the
attitude of the antenna is provided by at least one sensor for
sensing the position of the antenna.
33. A non-transitory computer-readable medium encoding program
instructions operable to cause one or more machine to perform
operations comprising: a. taking a first attitude measurement at a
first platform orientation to determine: i. a first vector {right
arrow over (d)} from the antenna to a satellite, the first vector
being determined based on the location of the platform as
determined by a position measuring device and a location of the
satellite; and ii. a second vector {right arrow over (d)}'.sub.i by
performing an alias transformation on the first vector {right arrow
over (d)} from a first reference frame to a second reference frame
based on the attitude of the platform; iii. a third vector {right
arrow over (d)}''.sub.i from the antenna to a satellite when the
antenna is peaked to the satellite, the third vector being
represented by coordinates defined with respect to a third
reference frame, the third vector {right arrow over (d)}''.sub.i
being determined based on information indicating the attitude of
the antenna; b. taking additional measurements at a plurality of
other platform orientations, each measurement determining a first
vector, second vector and third vector for the associated platform
orientation, resulting in a collection of second and third vectors;
c. determining a first rotation matrix based on the collection of
second and third vectors; d. determining a rotational offset
between the antenna and the platform based on the first rotation
matrix; and e. pointing the satellite antenna at the satellite
based on the determined rotational offset.
34. The method of claim 33, wherein the rotational offset is an
offset in roll, pitch and yaw with respect to the second reference
frame.
35. The method of claim 34, further including: a. using the roll,
pitch and yaw offset to determine a second rotation matrix; b.
receiving information indicating the location of the satellite; c.
receiving information indicating the location of the platform; d.
determining a fourth vector based on the location of the satellite
and the location of the platform; e. receiving attitude information
indicating the attitude of the platform; f. determining a fifth
vector by performing an alias transformation on the fourth vector
from the first reference frame to the second reference frame based
on the attitude of the platform; and g. determining a sixth vector
by performing an alias transformation on the fifth vector using the
second rotation matrix; and h. pointing the antenna to the
satellite based on the sixth vector.
36. An antenna control unit (AAM) for generating and providing
control signals to control the position of a satellite antenna
mounted on a mobile platform, including at least one processor
configured to: a. collect a plurality of attitude measurements,
each attitude measurement being determined by: i. receiving
information indicating the location of the platform and the
location of a satellite; ii. determining a first vector {right
arrow over (d)} from the satellite antenna to the satellite based
on the location of the platform and the location of the satellite,
the first vector {right arrow over (d)} being represented by
coordinates defined with respect to a first reference frame; iii.
receiving information indicating the attitude of the platform when
the platform is in a selected orientation; and iv. determining a
second vector {right arrow over (d)}'.sub.i by performing an alias
transformation on the first vector {right arrow over (d)}, the
alias transformation transforming the coordinates of the first
vector {right arrow over (d)} from the first reference frame to a
second reference frame based on the attitude of the platform when
in the selected orientation; v. receiving information indicating
the attitude of the satellite antenna when peaked to the satellite
with the platform in such one of the selected orientations; vi.
determining a third vector {right arrow over (d)}''.sub.i from the
antenna to the satellite based on the received information
indicating the attitude of the satellite antenna, the third vector
{right arrow over (d)}''.sub.i being represented in coordinates
defined with respect to a third reference frame; b. determine a
rotation matrix based on second vectors and third vectors
determined from the plurality of collected attitude measurements;
c. determine a roll, pitch, and yaw offset between the attitude of
the platform and the attitude of the satellite antenna based on the
rotation matrix; and d. point the satellite antenna at the
satellite based on the roll, pitch and yaw offsets.
Description
RELATED APPLICATIONS
[0001] This application claims priority from United States
provisional application entitled "Mobile Terminal Antenna Alignment
Using Arbitrary Orientation Attitude", Ser. No. 61/927,322, filed
14 Jan. 2014, which is incorporated herein by reference.
TECHNICAL FIELD
[0002] The disclosed method and apparatus relates to aligning an
antenna and more specifically to aligning an antenna mounted on a
mobile platform to the platform.
BACKGROUND
[0003] Satellite communication systems provide a means by which
data, including audio, video and various other sorts of data, can
be communicated from a transmitter at one location to a receiver at
another location. Satellite communication systems are currently
being used on mobile platforms, such as civilian airlines and
privately owned aircraft to provide entertainment and internet
access to the passengers. Military platforms, such as aircraft and
ships, currently use satellite communication systems to receive and
transmit various types of information, including strategic and
tactical information.
[0004] Satellite communication systems require an antenna to
receive signals from, and transmit signals to, a satellite. The
antenna typically must be pointed accurately at the satellite. A
satellite antenna positioner is typically used to point the antenna
at the satellite. It is common for these antenna positioners to
have two axes of motion (e.g., elevation and azimuth). In the case
of a system mounted on an aircraft, the elevation and azimuth that
will point the antenna to the satellite can be calculated if the
following information is known: (1) the location and attitude of
the aircraft; and (2) the location of the satellite, assuming the
relative alignment of the antenna to the body of the aircraft is
known. In most commercial airliners and military aircraft, the
attitude of an aircraft is determined by a position and attitude
measuring device (PAMD), such as an inertial reference unit
(IRU).
[0005] Such systems typically provide the attitude of the aircraft
in terms of three orthogonal axes: roll, pitch, and yaw. Errors in
alignment of the antenna with respect to the PAMD will cause
pointing errors (i.e., the antenna will not be pointed accurately
at the desired satellite when using information from the PAMD to
calculate the parameters, such as azimuth and elevation, for
pointing the antenna). These alignment errors can be defined as
roll, pitch and yaw errors. The antenna can be "peaked" to correct
for these errors for a particular orientation. Peaking involves
finding the antenna direction that results in the greatest signal
strength received from the satellite through the antenna. These
corrections are determined within the antenna positioner.
Accordingly, such corrections will be determined in the two axes of
elevation and azimuth used by the antenna positioner.
[0006] While the corrections can be converted from azimuth and
elevation to a three dimensional Cartesian coordinate system, a
problem exists in that such corrections will only be accurate for
that particular orientation of the mobile platform. Applying these
corrections to the azimuth and elevation calculated for other
orientations will not accurately point the antenna. In fact,
applying such corrections may result in even greater pointing
errors in some orientations.
[0007] It can be seen that accurately aligning the antenna to the
PAMD of an aircraft is important when using the PAMD output to
position a satellite antenna. However, performing the alignment
poses challenges. Therefore, there is currently a need for a simple
and accurate means by which to align a satellite antenna to a
mobile platform, such as an aircraft frame or PAMD within an
aircraft.
SUMMARY
[0008] Various embodiments of a method and apparatus for accurately
aligning a satellite antenna mounted on a mobile platform are
disclosed. In one embodiment of the disclosed method and apparatus,
the platform is an aircraft. However, the disclosed concepts can be
applied to other mobile platforms as well, such as ships, trucks,
trains, automobiles, and the like. In accordance with one
embodiment of the disclosed method and apparatus, the platform is
placed in a first orientation, which may be arbitrarily selected
for convenience. Measurements are made in the first orientation. In
the case in which the platform is an aircraft, the platform can be
placed in the first orientation during a pre-flight alignment
procedure, or while the aircraft is undergoing ground movement
(e.g., taxiing), or during flight.
[0009] The measurements are made by receiving the location of the
platform and the location of a satellite of interest. The location
of the platform and the satellite are used to determine a first
vector {right arrow over (d)} from the platform to the satellite.
The first vector {right arrow over (d)} is represented in
coordinates defined with respect to a topocentric reference frame.
An output from a Position and Attitude Measuring Device (PAMD),
such as an inertial reference unit (IRU), provides the attitude of
the platform. It should be noted that there may be an offset
between the platform reference frame and the PAMD reference frame.
However, for the purpose of this discussion, the platform reference
frame is assumed to be aligned with the PAMD reference frame. Any
such offset will be irrelevant, so long as the relationship between
the PAMD and the antenna reference frames remains fixed. A second
vector {right arrow over (d)}'.sub.i is determined by performing an
alias transformation on the first vector {right arrow over (d)}
based on the attitude output from the PAMD to transform the first
vector {right arrow over (d)} from the topocentric reference frame
to the second vector {right arrow over (d)}'.sub.i having
coordinates defined with respect to the platform reference frame
(i.e., PAMD reference frame).
[0010] In addition, an antenna control unit (ACU) peaks the
antenna. The orientation of the antenna when peaked is determined
based on the output from an antenna positioning motor or sensors
used to assist in positioning the antenna (i.e., directing the
antenna to a satellite). For example, in one embodiment in which
the antenna is positioned using an antenna positioning motor having
motion in azimuth and elevation, the azimuth and elevation that
result in the antenna receiving the strongest signal are used as
the orientation of the antenna. A third vector {right arrow over
(d)}''.sub.i pointing from the antenna to the satellite represented
in coordinates defined with respect to the antenna reference frame
is determined based on the orientation of the antenna when peaked
(i.e., the azimuth and elevation in the embodiment in which the
antenna motor operates in these two axes).
[0011] The measurements are repeated for several orientations. Once
measurements for an adequate number of orientations have been
collected, a matrix comprising the collection of second vectors
{right arrow over (d)}'.sub.i and a matrix comprising the
collection of third vectors {right arrow over (d)}''.sub.i are used
to determine a first rotation matrix. The first rotation matrix can
then be used to determine roll, pitch and yaw offsets between the
PAMD reference frame and the antenna reference frame.
[0012] A second rotation matrix is derived from the roll, pitch and
yaw offsets. The second rotation matrix is used to perform an alias
transformation on a vector in the PAMD reference frame to a vector
in the antenna reference frame. Accordingly, a vector calculated to
point from the platform to the satellite can be transformed to a
vector pointing from the antenna to the satellite in the antenna
reference frame. The vector in the antenna reference frame can be
used to generate coordinates (i.e., azimuth and elevation) to be
used in the antenna position motor to accurately point the antenna
to the satellite.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The disclosed method and apparatus, in accordance with one
or more various embodiments, is described with reference to the
following figures. The drawings are provided for purposes of
illustration only and merely depict examples of some embodiments of
the disclosed method and apparatus. These drawings are provided to
facilitate the reader's understanding of the disclosed method and
apparatus. They should not be considered to limit the breadth,
scope, or applicability of the claimed invention. It should be
noted that for clarity and ease of illustration these drawings are
not necessarily made to scale.
[0014] FIG. 1a is an illustration of the relevant components of a
satellite communication system in accordance with one embodiment of
the presently disclosed method and apparatus.
[0015] FIG. 1b is an illustration of an alternative embodiment of
the presently disclosed method and apparatus in which a Position
and Attitude Measurement Device (PAMD) is included within an
Antenna Alignment Module (AAM).
[0016] FIG. 2 is an illustration of a three-dimensional Cartesian
coordinate frame set in a topocentric reference frame.
[0017] FIG. 3 is an illustration of the aircraft and the associated
PAMD reference frame associated with the PAMD on board the
aircraft.
[0018] FIG. 4 is an illustration of a vector in a first reference
frame comprising an X.sub.1, Y.sub.1, and Z axis.
[0019] FIG. 5 is a simplified flow chart of the procedure used in
accordance with one embodiment of the disclosed method and
apparatus for determining the roll, pitch and yaw rotational
offsets between an antenna and a positioning and attitude
measurement device (PAMD) mounted in an aircraft.
[0020] FIG. 6 is a simplified flow chart of a procedure for using
the calculated roll, pitch and yaw offsets to direct an antenna at
a satellite.
[0021] The figures are not intended to be exhaustive or to limit
the claimed invention to the precise form disclosed. It should be
understood that the disclosed method and apparatus can be practiced
with modification and alteration, and that the invention should be
limited only by the claims and the equivalents thereof.
DETAILED DESCRIPTION
[0022] FIG. 1a is an illustration of the relevant components of a
satellite communication system 100 in accordance with one
embodiment of the presently disclosed method and apparatus. In the
illustrated embodiment, an antenna 102 is mounted on a mobile
platform. For the sake of illustration, the platform shown in FIG.
1a is an aircraft 103. However, it should be noted that the
platform could be any mobile platform, such as a truck, automobile,
ship, train or other such mobile platform.
[0023] FIG. 1a is intended to identify the relevant components of a
system and not to accurately represent the relative location or
size of the equipment within an aircraft. Furthermore, only those
components that are relevant to the presently disclosed method and
apparatus are depicted in FIG. 1a for the sake of simplicity.
Accordingly, the scale and relative location of the equipment
within an actual aircraft may vary significantly from what is
depicted in FIG. 1a. Furthermore, some components that are
necessary for a satellite communication system, but which are not
necessary for the disclosed method and apparatus for aligning an
antenna, are not shown in FIG. 1a.
[0024] An antenna positioning module, such as an antenna
positioning motor 104 is coupled to the antenna 102 to move the
antenna 102. Alternatively, the antenna positioning module is an
electronically steering module that directs the antenna beam. In
accordance with one embodiment of the disclosed method and
apparatus, the motor 104 moves the antenna in azimuth and
elevation. In an alternative embodiment, the positioning motor 104
may move the antenna in three axes or in different axes, such as
yaw and pitch. An antenna alignment module AAM 108 comprising an
antenna control unit (ACU) 115 provides control signals to the
motor 104 through a first output port 107. In one embodiment, a
radome 105 covers the antenna 102 and motor 104. Alternatively, the
motor 104 may be below the antenna 102 and inside the fuselage of
the aircraft. In another alternative embodiment, the antenna is
connected remotely by linkage that allows the motor 104 to control
the movement of the antenna 102. It will be understood by those
skilled in the art that any manner by which the antenna can be
positioned, including electronically steering the antenna, would be
within the scope of the disclosed method and apparatus. The motor
104 or electronic steering module may provide information regarding
the position of the antenna 102 back to the AAM 108 through an
input port 111.
[0025] In accordance with one embodiment of the disclosed method
and apparatus, signals received by the antenna 102 are coupled to a
low noise block (LNB) 110. In one such embodiment, the LNB 110
amplifies the signals. In one such embodiment, the LNB also
performs front end processing, such as filtering and/or frequency
down-conversion. The output of the LNB 110 is coupled to a modem
112. In one such embodiment, the modem 112 measures the received
power and provides an output signal 117 through an input port 109
to the AAM 108 indicating the received power. Alternatively, the
received power is measured within the LNB 110 or by another
component within the receive chain. Any device and manner can be
used to measure the received power and would be within the scope of
the disclosed method and apparatus. For the purposes of this
disclosure, received power is measured to provide feedback to
assist in pointing the antenna, as is discussed in greater detail
below.
[0026] In accordance with one embodiment of the presently disclosed
method and apparatus, an attitude determining device is present. In
one such embodiment, the attitude determining device is included
within a position and attitude measuring device (PAMD) 114 is
present (illustrated as being on board the aircraft 103). In
accordance with one embodiment of the disclosed method and
apparatus, the PAMD 114 is an inertial reference unit (IRU).
Alternatively, the PAMD 114 may be an inertial measurement unit
(IMU) or any other device capable of providing information
regarding position and attitude. It should be further noted that in
one embodiment of the disclosed method and apparatus, the PAMD 114
comprises two independent devices or systems, the attitude
determining device that determines attitude and a position
determining device that determines position. For example, a set of
gyroscopes can provide information regarding attitude. An
independent global positioning system (GPS) can provide information
regarding position. In any case, the PAMD 114 provides the attitude
and position of the aircraft 103 to the AAM 108. For the purposes
of this discussion, it is assumed that the PAMD 114 is aligned with
the platform (i.e., the aircraft 103). Any offset between the
platform and the PAMD 114 will be irrelevant, since all
measurements are made with respect to the PAMD 114, as long as the
relationship between the PAMD and the antenna remain unchanged. In
one embodiment, in addition to providing information that assists
with pointing and alignment of the antenna 102, the PAMD 114
provides real-time information that helps the pilot navigate and
operate the aircraft 103. Alternatively, two independent systems
are provided. The first such system provides information used for
alignment of the antenna 102 and the second for navigation. In
either case, in one embodiment, the PAMD 114 used for alignment of
the antenna 102 is assumed to be aligned with a topocentric frame
of reference. Alternatively, the PAMD 114 is aligned with a
reference frame that has a relationship with the topocentric
reference frame that is either known or that can be determined. In
yet another alternative embodiment, the PAMD 114 is aligned with a
reference frame that has a relationship with a reference frame in
which a satellite 106 can be located. In accordance with one
embodiment of the disclosed method and apparatus, the attitude of
the platform, the PAMD 114 and the antenna 102 remain essentially
unchanged as the platform changes attitude. It will be understood
that some change will occur due to flexing of the platform and the
structural components of the antenna mount, etc. In cases in which
the offset between the PAMD reference frame and the antenna
reference frame change over time due to structural changes due to
loading or aging, such differences can be accounted for by
re-aligning the antenna to the PAMD using the process disclosed
herein.
[0027] The AAM 108 receives information from the PAMD 114 through
an input port 109. In the embodiment shown in FIG. 1a, the
information is provided through the modem 112. However, in an
alternative embodiment, the PAMD 114 is directly connected to the
AAM 108. In one such embodiment, the information is provided over a
standard ARINC 429 bus. Routing the information provided by the
PAMD 114 through the modem allows the connection that is otherwise
required between the modem and the AAM 108 to be advantageously
exploited. FIG. 1b illustrates an embodiment in which the LNB 110,
modem 112, PAMD 114 and ACU 115, is all located within the AAM 108.
Alternatively, some, but not all, of these components are located
within the AAM 108. It should be noted that the functions of each
of these components can be performed by others of the components as
well. For example, in one embodiment of the disclosed method and
apparatus, a processor within the modem 112 determines the values
of some of the vectors associated with the alignment procedure.
Additionally, the functions associated with the PAMD 114 can be
performed by a PAMD within the AAM 108. An additional PAMD can also
be provided within the platform to assist with navigation of the
platform. In one embodiment, the additional PAMD also provides
information that is used by the AAM 108.
[0028] FIG. 2 is an illustration of a three dimensional Cartesian
coordinate frame 200 set in a topocentric reference frame. In this
example, the X axis 202 is aligned with the compass heading North,
the Y axis 204 is aligned with the compass heading East and the Z
axis 206 is aligned with an earth radian that emanates from the
origin of the reference frame and extends through the center of the
earth. This alignment is commonly known as North, East, Down (NED).
Each axis is orthogonal and forms a 90 degree angle with each of
the other axes. In accordance with one embodiment of the disclosed
method and apparatus, the origin of the topocentric reference frame
used by the PAMD 114 is the latitude and longitude of the aircraft
103. Altitude is assumed to be zero (i.e., the origin of the
topocentric reference frame is at earth surface).
[0029] FIG. 3 is an illustration of the aircraft 103 and an
associated PAMD reference frame 300 associated with the PAMD 114 on
board the aircraft 103. In this example, the X axis of the PAMD
reference frame 300 is along the longitudinal axis 302 of the
aircraft 103. The Y axis is along the lateral axis 304 of the
aircraft 103 The Z axis is along the vertical axis 306 of the
aircraft 103. Unlike the topocentric reference frame which remains
fixed in attitude with respect to earth, the PAMD reference frame
300 moves along with the aircraft 103. The attitude of the aircraft
103 is defined by the set of rotations in roll, pitch and yaw
between the PAMD reference frame 300 and the topocentric reference
frame 200. Roll is the rotation of the aircraft 301 about the X
axis. Pitch is the rotation of the aircraft 301 about the Y axis.
Yaw is the rotation of the aircraft 301 about the Z axis.
[0030] In one embodiment of the disclosed method and apparatus,
information indicating the attitude of the aircraft 103 is output
from the PAMD 114 in the form of three angular displacements. A
first angular displacement represents the rotation in roll, the
second represents the rotation in pitch and the third represents
the rotation in yaw.
[0031] In order to receive the satellite signals through the
antenna 102 with the maximum possible signal strength, the antenna
102 must be positioned to point at a transmitting satellite 106
(similarly for transmission from the antenna 102 to the satellite
106). When attempting to point an antenna 102 at a satellite 106, a
vector can be calculated from the antenna 102 to the satellite 106,
assuming known values for (1) the location of the satellite 106,
(2) the location of the antenna 102 and (3) the attitude of the
antenna with respect to the satellite 106. All of these factors can
be measured or computed. In particular, the locations of satellites
are well known and available in coordinates that are typically
represented in a topocentric reference frame. In accordance with
one embodiment of the disclosed method and apparatus, the location
of the satellite is provided to the AAM 108 from the modem 112
through the input port 109. Alternatively, the PAMD 114 is within
the AAM 108. In some embodiments of the presently disclosed method
and apparatus, the origin of the reference frame used to define the
location of the satellite 106 will be displaced from the origin of
the topocentric reference frame having an origin at the latitude
and longitude of the aircraft 103.
[0032] The location of the antenna 102 can be assumed to be the
location that is output by the PAMD 114 (i.e., any error due to the
fact that the antenna 102 may not be exactly collocated with the
PAMD 114 are assumed to be negligible and are thus ignored). With
this information, a unit vector {right arrow over (d)} can be
calculated which points from the antenna 102 to the satellite 106.
The vector {right arrow over (d)} is composed of three components,
dx, dy, dz, with respect to the topocentric reference frame having
its origin at the latitude and longitude of the aircraft 103. If
the aircraft 103 (and so the PAMD 114) is aligned with the
topocentric reference frame (i.e., the aircraft 103 is pointing
north with no pitch or roll with respect to the topocentric
reference frame), then the azimuth and elevation of the antenna 102
can be easily calculated directly from the vector {right arrow over
(d)}.
[0033] However, in the more general case, the aircraft 103 has an
attitude that is not aligned with the topocentric reference frame.
That is, the aircraft 103 has a heading other than North and may
have a pitch and roll offset as well. In this case, the vector
{right arrow over (d)} must be transformed using an alias
transformation. An alias transformation is defined as a
transformation of the coordinates of a vector from a first
coordinate system to a second coordinate system. The vector remains
in the same place and only the coordinate system changes (i.e., the
frame of reference used to represent the vector). Accordingly, a
vector having coordinates defined with respect to a first reference
frame can be represented as a vector having coordinates defined
with respect to a second reference frame.
[0034] FIG. 4 is an illustration of a vector 401 in a first
reference frame 200 comprising an X.sub.1 axis 202, a Y.sub.1 axis
204, and a Z axis 206. FIG. 4 further shows a rotation of the first
reference frame 200. In this example, rotating the first reference
frame 200 forms a second reference frame comprising an X.sub.2 axis
402, a Y.sub.2 axis 404, and the same Z axis 206. In the case shown
in FIG. 4, the first reference frame is rotated about only one axis
(i.e., the Z axis 206) in order to simplify the example. Therefore,
the Z axis 206 is common to both reference frames. In the example
of FIG. 4, the vector 401 lies in the X, Y plane of both the first
and second reference frames (i.e., the Z component of the vector
401 is zero in both frames of reference). In the first reference
frame 200, the vector 401 has a projection to the X axis of
approximately -0.707 (assuming the vector 401 to be a unit vector
forming an angle of 45 degrees between the X and Y axis). The
projection of the vector 401 on the Y axis is approximately 0.707.
If the first reference frame 200 is rotated -45 degrees about the Z
axis 206 (using the right-hand rule of thumb convention), then the
vector 401 has a projection on the X axis of -1.0 and a projection
on the Y axis of 0.0 in the second reference frame.
[0035] While in this example the transformation is easy to see, it
is typically necessary to determine the transformation more
generally. The alias transformation of a vector from a first
reference frame to a second reference frame can be calculated
as:
{right arrow over (d)}'.sub.i=M.sub.i{right arrow over (d)} Eq.
1
[0036] where {right arrow over (d)}'.sub.i is the vector 401 in the
second reference frame, {right arrow over (d)} is the vector 401 in
the first reference frame and M.sub.i is the rotation matrix shown
in Eq. 2 below. Thus, the rotation matrix M.sub.i of Eq. 2 is used
to perform the alias transformation of the vector 401 from the
first to the second reference frame. The index i is used to
distinguish a first orientation from subsequent orientations, each
orientation being referenced to the first reference frame.
M i ( R i , P i , Y i ) = [ cos ( P i ) * cos ( Y i ) cos ( P i ) *
sin ( Y i ) - sin ( P i ) sin ( R i ) * sin ( P i ) * cos ( Y i ) -
cos ( R i ) * sin ( Y i ) sin ( R i ) * sin ( P i ) * sin ( Y i ) +
cos ( R i ) * cos ( Y i ) sin ( R i ) * cos ( P i ) cos ( R i ) *
sin ( P i ) * cos ( Y i ) + sin ( R i ) * sin ( Y i ) cos ( R i ) *
sin ( P i ) * sin ( Y i ) - sin ( R i ) * cos ( Y i ) cos ( R i ) *
cos ( P i ) ] Eq . 2 ##EQU00001##
[0037] In the case of the example shown in FIG. 4 in which R.sub.i
is 0.degree., P.sub.i is 0.degree. and Y.sub.i is -45.degree., the
rotation matrix times the vector {right arrow over (d)} is equal
to:
M i d .fwdarw. = [ cos ( - 45 ) sin ( - 45 ) 0 - sin ( - 45 ) cos (
- 45 ) 0 0 0 1 ] [ - .707 .707 0 ] = [ .707 - .707 0 .707 .707 0 0
0 1 ] [ - .707 .707 0 ] = [ - .5 + - .5 - .5 + .5 0 ] = d .fwdarw.
i ' Eq . 3 ##EQU00002##
[0038] If both the location of the satellite 106 and the antenna
102 were known and the antenna 102 were well aligned to the PAMD
coordinate frame, the vector from the antenna 102 to the satellite
106 could be easily calculated by applying Eq. 2 and using the
roll, pitch and yaw output from the PAMD 114. However, when the
antenna 102 is mounted on an aircraft 103, as is the case in one
embodiment of the disclosed method and apparatus, the attitude of
the aircraft 103 (and so, typically the PAMD 114) will typically be
offset from the antenna frame of reference. That is, the antenna
102 typically will not be perfectly aligned with the PAMD 114.
[0039] Calculating the azimuth and elevation of the antenna
required to point the antenna 102 at the satellite 106 requires the
antenna 102 to be aligned with the PAMD 114. In accordance with one
procedure for aligning the antenna 102 to the PAMD 114, the
aircraft 103 must be taken onto as level a surface as possible. The
aircraft is oriented so that the output of the PAMD 114 in yaw
(heading) is 0.degree. (i.e., North). The antenna 102 is then
peaked to determine the azimuth and elevation that yields the
strongest signal from the satellite 106. Additional measurements
are made by physically repositioning the aircraft 103 to headings
of 90.degree., 180.degree. and 270.degree. based on heading
readings from the PAMD 114. If the aircraft is resting on perfectly
flat terrain, then the azimuth and elevation measurements will
directly translate to the roll, pitch and yaw offsets between the
antenna reference frame and the topocentric reference frame.
However, this method requires that the aircraft 103 be perfectly
level and that it be oriented very precisely to 0.degree.,
90.degree., 180.degree. and 270.degree..
[0040] Alternatively, an alignment procedure according to the
disclosed method and apparatus can be used in which the aircraft
103 is initially in any orientation. In accordance with this
procedure, a first vector {right arrow over (d)} from the antenna
102 to the satellite 106 is calculated in the topocentric reference
frame. Since the location of the satellite 106 and the location of
the aircraft 103 are both known in the topocentric reference frame,
this is easily accomplished. For the purpose of determining the
first vector {right arrow over (d)}, the difference between the
location of the aircraft 103 and the location of the antenna 102 is
considered negligible. Any difference in the location of the origin
of the topocentric reference frame used to define the location of
the satellite 106 and the origin of the reference frame used to
define the location of the aircraft 103 (i.e., the location output
of the PAMD 114) is easily managed by a simple translation of the
coordinates from one reference frame to the other.
[0041] Next, the first vector {right arrow over (d)} is transformed
by an alias transformation to the PAMD reference frame to determine
a second vector {right arrow over (d)}'.sub.i. This is done using
the alias transformation noted above in Eq. 1. The first vector
{right arrow over (d)} is multiplied with the rotation matrix
M.sub.i (R.sub.i, P.sub.i, Y.sub.i), of Eq. 2, where R.sub.i, is
the amount of roll as indicated by the PAMD 114, P.sub.i, is the
amount of pitch as indicated by the PAMD 114, and Y.sub.i is the
amount of yaw as indicated by the PAMD 114.
[0042] If the antenna 102 is aligned with the PAMD 114, the second
vector {right arrow over (d)}'.sub.i in the PAMD reference frame
could be directly converted to azimuth and elevation. However,
assuming there is a rotational offset between the reference frame
of the PAMD 114 and the reference frame of the antenna 102,
directly converting the vector in the PAMD reference frame to an
azimuth and elevation will result in an error in the calculation of
the azimuth and elevation of the antenna 102. The result is that
the antenna 102 will not be pointed directly at the satellite 106.
The error can be measured by peaking the antenna 102 and reading
the resulting azimuth and elevation directly from the antenna
positioning motor 104 or a sensor on the antenna 102. However,
correcting the error in this manner is only valid for that
particular orientation.
[0043] In order to provide a more general solution that will be
valid in all orientations, the following method and apparatus is
disclosed for providing a best fit rotation matrix between the PAMD
reference frame and the antenna reference frame.
[0044] In accordance with one embodiment of the disclosed method
and apparatus, the antenna 102 is peaked to determine the azimuth
and elevation setting of the positioning motor 104 that results in
the maximum signal strength being received in a signal from the
satellite 106 with the aircraft in a first orientation. Signal
strength can be determined based on the amplitude, signal to noise
ratio (SNR), amount of received power, or other such metric. In
accordance with one embodiment, the azimuth and elevation are
determined by the control signals provided to the antenna
positioning motor 104. Alternatively, the azimuth and elevation are
read directly from the motor 104. In an alternative embodiment, the
azimuth and elevation are read from an antenna position sensor (not
shown) coupled to the antenna 102 or to the antenna positioning
motor 104.
[0045] In accordance with one embodiment of the disclosed method
and apparatus, a step track technique is used to "peak" the
antenna. In one such step track peaking scheme, the antenna 102 is
positioned roughly toward the satellite 106. This is done using a
rough estimate of the pointing elevation and azimuth to be applied
to the motor 104. In one embodiment of the disclosed method and
apparatus, the offset between the PAMD 114 reference frame and the
antenna 102 will not be so great that the satellite signal is not
detectable. Therefore, in accordance with one embodiment, the
azimuth and elevation calculated under the assumption that there is
no offset between the PAMD reference frame and the antenna
reference frame is a sufficiently accurate estimate at which to
begin the peaking procedure.
[0046] A measurement is made of the power received through the
antenna. The position of the antenna 102 is then changed in
elevation by one "step". The AAM 108 directs the antenna 102 to
implement the peaking technique based on the received power
measurements provided from the modem 112. In an alternative
embodiment, the received power is measured by a device other than
the modem 112. It will be understood by those skilled in the art
that a device placed essentially anywhere along the receive chain
can be used to measure the received power.
[0047] For example, if the amount of received power drops after
changing the elevation of the antenna 102, the antenna 102 is moved
in the opposite direction. In one embodiment, the antenna 102 moves
by two steps. If the amount of received power increases, the
antenna is moved another step further in that direction. Another
power measurement is made. Each time the amount of receive power
increases, the antenna is moved another "step" in the same
direction. Upon measuring a drop in the power, the antenna
direction is reversed and moved one step back. Once the peak power
measurement for elevation has been detected, the antenna begins a
similar search for the peak in azimuth. If the initial azimuth
position was not the peak, then the search in elevation is
repeated. If the antenna was not at the peak elevation, then the
search for the peak in azimuth is again repeated. This process will
continue until both the elevation and the azimuth are at the peak
received power.
[0048] It will be clear to those skilled in the art that this is a
simplistic step track peaking algorithm. Many modifications to this
procedure can be implemented to improve the likelihood that the
antenna is at the best pointing elevation and azimuth. Furthermore,
other peaking techniques can be employed, such as, but not limited
to, one technique known commonly as conical scan (conscan).
[0049] In addition to determining the azimuth and elevation of the
antenna 102 at peak for the first orientation of the aircraft 103,
an attitude reading from the PAMD 114 is taken. In accordance with
one embodiment of the disclosed method and apparatus, the aircraft
103 is positioned in various additional orientations. In one
embodiment of the disclosed method and apparatus, the additional
orientations are achieved by rotating the aircraft on the ground.
Alternatively, the additional orientations could be achieved by a
relative change in orientation with respect to the satellite, such
as using a different satellite with the aircraft remaining in a
fixed orientation with respect to the earth. In one case in which
the aircraft is moved, the heading of the aircraft 103 is changed
for each additional orientation. This can be done by taxiing the
aircraft or towing the aircraft to move the aircraft to the new
orientation. In yet another embodiment, the aircraft 103 can be in
flight during the procedure. Accordingly, as the aircraft 103
maneuvers over the course of the flight, the orientation will
change, allowing additional measurements to be made. In one such
embodiment, the rate of change of the attitude output from the PAMD
114 is determined and used to estimate the attitude of the aircraft
103 at particular times when the antenna 102 is peaked. For
example, a determination of the attitude of the platform is made at
a first time prior to the aircraft being in the first orientation
(i=1) (i.e., the first orientation at which the antenna 102 is
peaked). In addition, a determination as to the rate of change of
the attitude of the aircraft 103 is made at the first time. A
determination is then made as to the attitude of the aircraft 103
at a second time when the aircraft is in the first orientation. The
determination is made from the attitude and rate of change of the
aircraft 103 determined at the first time. Accordingly, from the
attitude and the rate of change in the attitude at a first time, an
extrapolation can be made to determine the attitude at a second
time that occurs either before or after the first time. For each
particular orientation, the antenna 102 is peaked to determine the
azimuth and elevation that results in the highest received signal
level. The attitude output of the PAMD 114 is associated with the
azimuth and elevation for that particular orientation. The azimuth
and elevation at each orientation are converted to a third vector
{right arrow over (d)}''.sub.i in a Cartesian coordinate system in
the antenna reference frame using the following relationship, where
.alpha. is azimuth and .epsilon. is elevation:
d''.sub.ix=cos .epsilon..sub.i cos .alpha..sub.i
d''.sub.iy=cos .epsilon..sub.i sin .alpha..sub.i
d''.sub.iz=-sin .epsilon..sub.i Eq. 4
[0050] Accordingly, for each attitude there is a first vector
{right arrow over (d)} determined by the location of the platform
103 and the location of the satellite 106 and represented in
coordinates defined with respect to the first reference frame
(i.e., the topocentric reference frame). In addition, there is a
second vector {right arrow over (d)}'.sub.i represented by
coordinates defined with respect to the second reference frame
(i.e., PAMD reference frame) and a third vector {right arrow over
(d)}''.sub.i represented by coordinates defined with respect to the
third reference frame (i.e., antenna reference frame). The
collection of second vectors {right arrow over (d)}'.sub.i forms a
first matrix D' and the collection of third vectors {right arrow
over (d)}''.sub.i forms a second matrix D''. If each collection of
second and third vectors has no measurement noise or other source
of error or inconsistency, then the first matrix is related to the
second by the following equation, where T is a rotation matrix:
D''=T D' Eq. 5
[0051] Once a sufficient number of measurements for {right arrow
over (d)}'.sub.i and {right arrow over (d)}''.sub.i have been
gathered, the rotation matrix T can be solved. By solving for T,
the general transformation from the PAMD reference frame to the
antenna reference frame can be calculated (i.e., the offset in each
of the three axes, roll, pitch and yaw can be determined and used
to calculate an alias transformation). Thus, the output of the PAMD
114 can be used to calculate the azimuth and elevation needed to
point the antenna 102 to the satellite 106.
[0052] Solving for T matches the form of Wahba's Problem. There are
several ways known to solve Wahba's Problem. One way is to use
Singular Value Decomposition to determine the pseudoinverse of the
collection of vectors D' in the PAMD reference frame. By
multiplying each side of equation Eq. 5 by the pseudoinverse
D'.sup.+ of D', the following equations result:
D''=T D'
D'' D'.sup.+=T D' D'.sup.+
T= D'' D'.sup.+ Eq. 6
[0053] The pseudoinverse can be calculated by using the elements of
the singular value decomposition (SVD) of D'.
D'=USV*
D'.sup.+=VS.sup.+U* Eq. 7
[0054] The pseudoinverse of S may be computed by taking the
transpose of the matrix formed with diagonal elements equal to the
reciprocal of the diagonal elements of S. For a collection of
measurements that are noisy or that have other errors, use of the
pseudoinverse will produce a least-squares estimate of the
rotation.
{circumflex over (T)}= D'' D'.sup.+, where {circumflex over (T)} is
the least squares estimate. Eq. 8
[0055] The elements of {circumflex over (T)} may be used to derive
the roll, pitch and yaw offsets to the vector {right arrow over
(d)}'.sub.i output from the PAMD 114 using the relationships of Eq.
9 and Eq. 10. {circumflex over (T)} is interpreted as the product
of Roll, Pitch, and Yaw rotations. The composite rotation matrix is
given as:
T ( R 0 , P 0 , Y 0 ) = [ r 11 r 12 r 13 r 21 r 22 r 32 r 31 r 32 r
33 ] = [ cos ( P 0 ) * cos ( Y 0 ) cos ( P 0 ) * sin ( Y 0 ) - sin
( P 0 ) sin ( R 0 ) * sin ( P 0 ) * cos ( Y 0 ) - sin ( R 0 ) * sin
( P 0 ) * sin ( Y 0 ) + cos ( R 0 ) * cos ( Y 0 ) sin ( R 0 ) * cos
( P 0 ) cos ( R 0 ) * sin ( Y 0 ) cos ( R 0 ) * sin ( P 0 ) * cos (
Y 0 ) + cos ( R 0 ) * sin ( P 0 ) * sin ( Y 0 ) - sin ( R 0 ) * cos
( Y 0 ) cos ( R 0 ) * cos ( P 0 ) sin ( R 0 ) * sin ( Y 0 ) ] Eq .
9 ##EQU00003##
[0056] From Eq. 9, one can see that the solutions to the Roll,
Pitch and Yaw rotations are:
Y.sub.0=tan.sup.-1(r.sub.12/r.sub.11)
P.sub.0=tan.sup.-1(-r.sub.13/ {square root over
(r.sub.23.sup.2+r.sub.33.sup.2)})
R.sub.0=tan.sup.-1(r.sub.23/r.sub.33) Eq. 10
[0057] A vector that is initially in the PADM reference frame
(i.e., a vector derived in the topocentric reference frame and
translated to the PADM reference frame) can be further transformed
by an alias transform to the antenna reference frame using
knowledge of the roll, pitch and yaw rotations provided in Eq.
10.
[0058] FIG. 5 is a simplified flow chart of the procedure used in
accordance with one embodiment of the disclosed method and
apparatus for determining the roll, pitch and yaw rotational
offsets between an antenna 102 and a PAMD 114 mounted in an
aircraft.
[0059] In STEP 501, an initial measurement is made with the
aircraft 103 in a first orientation. Taking the initial measurement
includes having a processor within the AAM 108 determine a first
vector {right arrow over (d)}. The first vector {right arrow over
(d)} is represented using coordinates defined with respect to a
first reference frame (i.e., a topocentric reference frame). The
first vector {right arrow over (d)} is determined from the location
of the aircraft 103 and the location of the satellite 106. In
accordance with one embodiment of the disclosed method and
apparatus, both the location of the aircraft 103 and the location
of the satellite 106 are represented by coordinates defined with
respect to a first reference frame (e.g., a topocentric reference
frame). In an alternative embodiment, the determination of the
first vector can be done by a processor that is not on board the
aircraft. Information regarding the location of the aircraft 103
and the location of the satellite 106 are provided to such a
processor.
[0060] The process of taking the initial measurement also includes
the AAM 108 using information from the PAMD 114 indicating the
attitude of the aircraft with the aircraft 103 in the first
orientation. The information from the PAMD 114 is represented with
coordinates defined with respect to a first reference frame. The
processor within the PAMD 114 determines a second vector {right
arrow over (d)}'.sub.i by performing an alias transformation on the
first vector {right arrow over (d)}. The alias transformation
transforms the representation of the first vector {right arrow over
(d)} from coordinates defined with respect to the first reference
frame to coordinates defined with respect to a second reference
frame (i.e., the PAMD reference frame). The transformation is
performed based on the relative rotation of the second reference
frame with respect to the first reference frame. The relative
rotation is determined by the attitude of the aircraft 103 in the
first orientation (see Eq. 1 above). The attitude of the aircraft
is provided by the PAMD 114. In one embodiment, the transformation
is performed within the AAM 108. In an alternative embodiment, the
transformation is performed by a processor that is not on board the
aircraft 103. Information necessary to perform the transformation
is provided to such a process to enable the transformation to be
performed.
[0061] It should be noted that the first vector {right arrow over
(d)} does not take into account the orientation of the aircraft
103, but is determined based only on the location of the aircraft
103 and the location of the satellite 106. Therefore, in the case
in which the aircraft 103 remains at the same location for each
orientation, there is no index i associated with the first vector
{right arrow over (d)}. However, if the location of the aircraft or
the satellite changes from one orientation to another, the change
in location can be taken into account. In that case, the first
vector {right arrow over (d)} would be represented as {right arrow
over (d.sub.i)} to indicate the value of the first vector at each
orientation i.
[0062] In addition, during the initial measurement, the processor
records the azimuth and elevation of the antenna 102 when the
antenna 102 is directed at the satellite 106. In accordance with
one embodiment of the disclosed method and apparatus, the antenna
102 is directed at the satellite 106 by peaking the antenna 102 to
receive the strongest signal possible from the satellite 106. In
one embodiment of the disclosed method and apparatus, information
regarding the attitude of the antenna 102 is provided to the AAM
108. For example, in one embodiment of the disclosed method and
apparatus, the azimuth and elevation of the positioning motor 104
that results in the antenna 102 receiving the strongest signal from
the satellite 106 is provided to the AAM 108. In another embodiment
in which the antenna is electronically steered, the attitude of the
antenna 102 is the direction of the electronic bore sight or
information from which the direction of the antenna bore sight can
be derived. Based on the information received by the AAM 108, the
processor within the AAM 108 determines a third vector {right arrow
over (d)}''.sub.i that points from the antenna 102 to the satellite
106. The third vector {right arrow over (d)}''.sub.i is represented
in Cartesian coordinates defined with respect to a third reference
frame (i.e., the antenna reference frame). In an alternative
embodiment, the attitude of the antenna is provided to a processor
that is not on-board the aircraft 103. In accordance with such an
embodiment, the third vector {right arrow over (d)}''.sub.i is
determined by such a processor.
[0063] An additional measurement is taken with the aircraft 103 in
a second orientation (STEP 503). In similar fashion to the initial
measurement, the additional measurement is taken by peaking the
antenna 102, determining the antenna azimuth and elevation and
recording the output of the PAMD 114 at the second orientation and
determining first, second and third vectors {right arrow over
(d.sub.2)}, {right arrow over (d.sub.2)}', {right arrow over
(d.sub.2)}''. Note that for the case in which the aircraft 103
remains essentially in the same location, but only changes attitude
from one orientation to another, the value {right arrow over
(d)}={right arrow over (d.sub.1)}={right arrow over
(d.sub.2)}={right arrow over (d.sub.i)}, for all i
orientations.
[0064] A determination is made as to whether enough measurements
have been taken (STEP 505). If more measurements are desired, then
the process repeats STEP 503 with the aircraft 103 in different
orientations. It should be noted that in accordance with one
embodiment of the disclosed method and apparatus, the particular
orientations at which measurements are taken are essentially
arbitrary. In addition, the particular number of measurements to be
made will depend upon the desired accuracy. In accordance with one
embodiment, eight measurements are made at various orientations
distributed approximately evenly about the yaw axis 306 of the
aircraft 103 (see FIG. 3). Alternatively, various factors are used
to influence the selection of orientations at which to take each of
the measurements.
[0065] One such factor is the relative deviation from the other
orientations at which measurements have been (or are to be) taken.
In some embodiments, measurements are taken at orientations that
are spaced relatively evenly over the 360.degree. of rotation
possible in each axis (roll, pitch and yaw). In other embodiments,
measurements are taken at relatively arbitrary orientations during
operation of the aircraft 103, including while taxiing, or in
flight, or both. The measurements may be taken over a span of time.
It should be noted that a reasonably accurate determination of the
offsets in roll, pitch and yaw between the reference frame of the
antenna 102 and the aircraft 103 (or PAMD 114) can be made based on
orientations resulting from rotating the aircraft 103 about only
one axis, such as yaw. The offsets can be determined initially
prior to operation of the satellite communication system, early in
the operation of that system, or at periodic intervals during
operation. In one embodiment in which offsets are updated
periodically, the updates can be used to learn and correct minor
changes in alignment over time, including changes in the frame of
the aircraft, differing conditions (e.g., when the aircraft is on
landing gear and when in the air, when the aircraft has differing
loads, etc.).
[0066] As noted above, an alignment procedure may be performed in
which the aircraft 103 is placed in 8 different orientations, each
orientation having a heading spaced evenly around the 360.degree.
of the compass. The roll and pitch of the aircraft 103 need not be
tightly controlled. Accordingly, in one such embodiment, the
aircraft 103 is turned to each compass heading at which a
measurement is to be taken. In one embodiment of the disclosed
method, the particular orientations selected are not critical,
allowing for a relatively fast and simply procedure to be
implemented for determining the offsets in roll, pitch and yaw
between the reference frame of the antenna 102 and the aircraft 103
(or PAMD 114).
[0067] Once a sufficient number of measurements (i.e., vectors
{right arrow over (d)}', {right arrow over (d)}'') have been
collected, a composite rotation matrix {circumflex over (T)} is
calculated based on the relationships shown above in Eq. 5 through
Eq. 8 (STEP 507). The roll, pitch and yaw offsets of the antenna
reference frame with respect to the PAMD reference frame are then
calculated based on the values presented in the composite rotation
matrix {circumflex over (T)} (STEP 509). In one embodiment of the
disclosed method and apparatus, the calculation of the composite
rotation matrix {circumflex over (T)} is made by a processor that
is not on-board the aircraft 103. The resulting roll, pitch and yaw
offsets are then transmitted back to the aircraft 103 to be used to
direct an antenna 102 or they are used to perform a correction to
the antenna positioning information and then transmitted to the
aircraft 103.
[0068] FIG. 6 is a simplified flow chart of a procedure for using
the calculated roll, pitch and yaw offsets determined from the
first, second and third vectors of FIG. 5 to direct an antenna at a
satellite. Initially, the output of the PAMD 114 is received (STEP
601). The output of the PAMD 114 includes the location and attitude
of the PAMD 114 in coordinates defined with respect to the PAMD
reference frame. From the location of the PAMD 114 and the location
of the satellite 106, a fourth vector {right arrow over (d)} from
the PAMD 114 to the satellite 106 can be calculated in coordinates
defined with respect to the topocentric reference frame (STEP 603).
An alias transformation is then performed on the fourth vector
{right arrow over (d)} to transform the coordinates of the vector
{right arrow over (d)} to the PAMD reference frame. The alias
transformation is performed by applying Eq. 2 to the attitude
information provided from the PAMD 114 to generate a first rotation
matrix M.sub.i (STEP 605).
[0069] The vector {right arrow over (d)} represented by coordinates
defined with respect to the topocentric reference frame is then
multiplied by the first rotation matrix M.sub.i. The result is a
fifth vector {right arrow over (d)}'.sub.i that points from the
PAMD 114 to the satellite 106. The fifth vector {right arrow over
(d)}'.sub.i is represented using coordinates defined with respect
to the PAMD reference frame (STEP 607).
[0070] A second rotation matrix {circumflex over (T)} is generated
(STEP 609) by applying the roll, pitch and yaw offsets determined
in STEP 509 of FIG. 5 to Eq. 9. The fifth vector {right arrow over
(d)}'.sub.i is then multiplied by the second rotation matrix
{circumflex over (T)} to transform coordinates of the fifth vector
to the antenna reference frame (STEP 611). The result is a sixth
vector {right arrow over (d)}''.sub.i that points from the antenna
102 to the satellite 106 represented in Cartesian coordinates
defined with respect to the antenna reference frame. The sixth
vector {right arrow over (d)}''.sub.i is then converted to
coordinates represented with respect to azimuth and elevation. The
azimuth and elevation of the vector {right arrow over (d)}''.sub.i
are then provided to the positioning motor 104 to point the antenna
102 to the satellite 106 (STEP 613).
[0071] It should be noted that in addition to the offsets in roll,
pitch and yaw, a constant error in the elevation positioner may
exist which produces an error in the elevation and azimuth
determined by the procedure of FIG. 5 and FIG. 6. In accordance
with one embodiment of the disclosed method and apparatus, it is
desirable to account for this error as well. One source of such a
constant elevation error is a misalignment of a motor stop in the
positioning motor 104. Such a constant elevation error introduces a
translation error. The translation error comes from the fact that
the elevation offset will corrupt the collection of measurements
used to derive the vector {right arrow over (d)}''.sub.i. As noted
above, the vector {right arrow over (d)}''.sub.i points from the
antenna 102 to the satellite 106 in Cartesian coordinates in the
antenna reference frame.
[0072] One way to estimate the error in the elevation measurements
made when the antenna is peaked to the satellite is to multiply the
vector {right arrow over (d)}''.sub.i by the transpose of an
orthogonalized version of {circumflex over (T)} and further by the
transpose of the rotation matrix M.sub.i. Accordingly, the error in
elevation measurements, {tilde over (w)}.sub.i is:
{tilde over (w)}.sub.i=M.sub.i.sup.T{tilde over (T)}.sup.T{right
arrow over (d)}''.sub.i Eq. 11
[0073] Orthogonalizing the matrix {circumflex over (T)} effectively
strips out the elevation offset information from the matrix
{circumflex over (T)}. One way to orthogonalize the matrix is to
compute the roll, pitch and yaw offsets. The roll, pitch and yaw
offsets are then used to construct a rotation matrix as
follows:
T ~ ( R 0 , P 0 , Y 0 ) = [ r 11 r 12 r 13 r 21 r 22 r 32 r 31 r 32
r 33 ] = [ cos ( P 0 ) * cos ( Y 0 ) cos ( P 0 ) * sin ( Y 0 ) -
sin ( P 0 ) sin ( R 0 ) * sin ( P 0 ) * cos ( Y 0 ) - sin ( R 0 ) *
sin ( P 0 ) * sin ( Y 0 ) + cos ( R 0 ) * cos ( Y 0 ) sin ( R 0 ) *
cos ( P 0 ) cos ( R 0 ) * sin ( Y 0 ) cos ( R 0 ) * sin ( P 0 ) *
cos ( Y 0 ) + cos ( R 0 ) * sin ( P 0 ) * sin ( Y 0 ) - sin ( R 0 )
* cos ( Y 0 ) cos ( R 0 ) * cos ( P 0 ) sin ( R 0 ) * sin ( Y 0 ) ]
Eq . 12 ##EQU00004##
[0074] Another way to orthogonalized the matrix {circumflex over
(T)} is to apply the Singular Value Decomposition to {circumflex
over (T)}. Omitting the S component will result in an orthogonal
matrix {tilde over (T)}.
{circumflex over (T)}=USV*
{tilde over (T)}=UV* Eq. 13
[0075] Other statistical shape analysis procedures may be used,
such as Procrustes analysis. For example, the Matlab.RTM.
statistics toolbox function PROCRUSTES may be used to estimate
{tilde over (T)}. In accordance with this approach:
[dd,Z,tr]=procrustes(X,Y,`Scaling`,false,`Reflection`,false) Eq.
14
[0076] where X is the transpose of the matrix with columns that are
the measured direction vectors in the antenna reference frame; and
Y is the transpose of the matrix with columns that are the
direction vectors in the PAMD reference frame. The best fit
rotation matrix will be returned as `tr.T`. Note that the
Procrustes function determines the matrix that fits the form:
D''.sup.T= D''.sup.T{circumflex over (T)}.sup.T Eq. 15
[0077] In one embodiment in which Procrustes or other statistical
shape analysis methods are used, the roll, pitch and yaw offsets
may be computed directly from the orthogonal matrix as well. The
elements of T may be used to derive the roll, pitch and yaw offsets
of the antenna positioner relative to the PAMD 114.
T ( R 0 , P 0 , Y 0 ) = [ r 11 r 12 r 13 r 21 r 22 r 32 r 31 r 32 r
33 ] = [ cos ( P 0 ) * cos ( Y 0 ) cos ( P 0 ) * sin ( Y 0 ) - sin
( P 0 ) sin ( R 0 ) * sin ( P 0 ) * cos ( Y 0 ) - sin ( R 0 ) * sin
( P 0 ) * sin ( Y 0 ) + cos ( R 0 ) * cos ( Y 0 ) sin ( R 0 ) * cos
( P 0 ) cos ( R 0 ) * sin ( Y 0 ) cos ( R 0 ) * sin ( P 0 ) * cos (
Y 0 ) + cos ( R 0 ) * sin ( P 0 ) * sin ( Y 0 ) - sin ( R 0 ) * cos
( Y 0 ) cos ( R 0 ) * cos ( P 0 ) sin ( R 0 ) * sin ( Y 0 ) ] Eq .
16 ##EQU00005##
[0078] The solutions are then
Y.sub.0=tan.sup.-1(r.sub.12/r.sub.11)
P.sub.0=tan.sup.-1(-r.sub.13/ {square root over
(r.sub.23.sup.2+r.sub.33.sup.2)})
R.sub.0=tan.sup.-1(r.sub.23/r.sub.33) Eq. 17
[0079] Alternatively, since the vector {right arrow over
(d)}''.sub.i has the elevation error, multiplying it as noted in
Eq. 11 will result in a vector {tilde over (w)}.sub.i. The z
component of the vector {tilde over (w)}.sub.i can be used to
calculate the elevation angle {tilde over (.epsilon.)}.sub.i for
each measurement i as follows:
{tilde over (.epsilon.)}.sub.i=sin.sup.-1(w.sub.iz) Eq. 18
[0080] The elevation offset can be determined by taking the average
of the difference between the elevations {tilde over
(.epsilon.)}.sub.i for each measurement i and the ideal topocentric
elevation angle {tilde over (.epsilon.)}.sub.o (i.e., the elevation
from the PAMD 114 to the satellite absent any offset or constant
elevation error).
.DELTA. = 1 N i = 1 N ~ i - 0 Eq . 19 ##EQU00006##
[0081] Once the constant elevation error .DELTA..epsilon. is
determined, the roll, pitch and yaw offsets can be recalculated
using elevation angles that have been corrected for the constant
elevation error .DELTA..epsilon..
[0082] Although the disclosed method and apparatus is described
above in terms of various examples of embodiments and
implementations, it should be understood that the particular
features, aspects and functionality described in one or more of the
individual embodiments are not limited in their applicability to
the particular embodiment with which they are described. For
example, it is possible to use quaternions to express the
relationships of the different reference frames to one another and
thus determine the offset between the antenna reference frame and
the PAMD reference frame by taking measurements at various
orientations as described above. Furthermore, some or all aspects
of the disclosed method and apparatus may be implemented in
hardware or software, or a combination of both (e.g., programmable
logic arrays). Various general purpose computing machines may be
used with programs written in accordance with the teachings herein.
Alternatively, a special purpose computer or special-purpose
hardware (such as integrated circuits) may be used to perform
particular functions. Thus, the disclosed method and apparatus may
be implemented in one or more computer programs executing on one or
more programmed or programmable computer systems.
[0083] Each such computer program may be stored on or downloaded to
(for example, by being encoded in a propagated signal and delivered
over a communication medium such as a network) a tangible,
non-transitory storage media or device (e.g., solid state memory or
media, or magnetic or optical media) readable by a general or
special purpose programmable computer, for configuring and
operating the computer when the storage media or device is read by
the computer system to perform the procedures described herein. The
inventive system may also be considered to be implemented as a
computer-readable storage medium, configured with a computer
program, where the storage medium so configured causes a computer
system to operate in a specific and predefined manner to perform
the functions described herein. Thus, the breadth and scope of the
claimed invention should not be limited by any of the examples
provided in describing the above disclosed embodiments.
[0084] Terms and phrases used in this document, and variations
thereof, unless otherwise expressly stated, should be construed as
open ended as opposed to limiting. As examples of the foregoing:
the term "including" should be read as meaning "including, without
limitation" or the like; the term "example" is used to provide
examples of instances of the item in discussion, not an exhaustive
or limiting list thereof; the terms "a" or "an" should be read as
meaning "at least one," "one or more" or the like; and adjectives
such as "conventional," "traditional," "normal," "standard,"
"known" and terms of similar meaning should not be construed as
limiting the item described to a given time period or to an item
available as of a given time, but instead should be read to
encompass conventional, traditional, normal, or standard
technologies that may be available or known now or at any time in
the future. Likewise, where this document refers to technologies
that would be apparent or known to one of ordinary skill in the
art, such technologies encompass those apparent or known to the
skilled artisan now or at any time in the future.
[0085] A group of items linked with the conjunction "and" should
not be read as requiring that each and every one of those items be
present in the grouping, but rather should be read as "and/or"
unless expressly stated otherwise. Similarly, a group of items
linked with the conjunction "or" should not be read as requiring
mutual exclusivity among that group, but rather should also be read
as "and/or" unless expressly stated otherwise. Furthermore,
although items, elements or components of the disclosed method and
apparatus may be described or claimed in the singular, the plural
is contemplated to be within the scope thereof unless limitation to
the singular is explicitly stated.
[0086] Additionally, the various embodiments set forth herein are
described with the aid of block diagrams, flow charts and other
illustrations. As will become apparent to one of ordinary skill in
the art after reading this document, the illustrated embodiments
and their various alternatives can be implemented without
confinement to the illustrated examples. For example, block
diagrams and their accompanying description should not be construed
as mandating a particular architecture or configuration. Further,
some of the steps described above may be order independent, and
thus can be performed in an order different from that described.
Various activities described with respect to the embodiments
identified above can be executed in repetitive, serial, or parallel
fashion.
* * * * *